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Neusel M.D. — Invariant Theory of Finite Groups
Neusel M.D. — Invariant Theory of Finite Groups

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Название: Invariant Theory of Finite Groups

Автор: Neusel M.D.

Аннотация:

The questions that have been at the center of invariant theory since the 19th century have revolved around the following themes: finiteness, computation, and special classes of invariants. This book begins with a survey of many concrete examples chosen from these themes in the algebraic, homological, and combinatorial context. In further chapters, the authors pick one or the other of these questions as a departure point and present the known answers, open problems, and methods and tools needed to obtain these answers. Chapter 2 deals with algebraic finiteness. Chapter 3 deals with combinatorial finiteness. Chapter 4 presents Noetherian finiteness. Chapter 5 addresses homological finiteness. Chapter 6 presents special classes of invariants, which deal with modular invariant theory and its particular problems and features. Chapter 7 collects results for special classes of invariants and coinvariants such as (pseudo) reflection groups and representations of low degree. If the ground field is finite, additional problems appear and are compensated for in part by the emergence of new tools. One of these is the Steenrod algebra, which the authors introduce in Chapter 8 to solve the inverse invariant theory problem, around which the authors have organized the last three chapters. The book contains numerous examples to illustrate the theory, often of more than passing interest, and an appendix on commutative graded algebra, which provides some of the required basic background. There is an extensive reference list to provide the reader with orientation to the vast literature.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 371

Добавлена в каталог: 28.11.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Pseudoreflection representation      186
Pseudoreflections      186
Pseudoreflecton      19
Pullback technique      74
Purely transcendental      25
q-Boolean algebra      285 295 296
Q-polynomial      152
Quaternion group      94 216 217
Radical (of an ideal)      322
Rational function      66
Rational representation      27
Reduced monomial      70
Reductive algebraic group      13
Regular element      137
Regular representation      7 10 17 24 83 161 194
Regular sequence      114 129 139 173
Regular sequence on a module      139
Relative invariant      5 195
Relative invariants      6
Relative Noether bound      203
Relative transfer      33 140
Remembering map      13
Representable functor      248
Representation of degree 2      172
Representation over $\mathbb{Q}$      27
Representing module      248
Residue calculation      232
Residue field at a prime ideal      304
Resolution degree      116
Reverse Landweber — Stong conjecture      254
Ring of formal power series over A      22
Ring of invariants      4
S(G)      51
Schur index      187
Second Fundamental Theorem      25
Semitensor product      247
Shephard — Todd List      188
Shephard — Todd theorem      190
Sign-symmetric      5
Signum      5
Simple group      27
Socle      144
Socle filtration      102
Socle length      102
Solvable group      17 203 208
Solvable groups      23
Special linear group      54
Special monomial      70
Special orthogonal group      309
Spectral sequence      174
Stabilizer subgroup      288 307
Stabilizer subgroups and the $\mathrm{T}$-functor      288
Stable      36
Stable invariants      8 11 177
Stable under G-action      36
Standard references, commutative algebra      30
Stanley, R.P.      53
Steenrod algebra      227 228 230 231 255
Steenrod operations      21 22 152 229
Steenrod powers of Dickson polynomials      257
Steenrod reduced power operations      22 229
Steenrod squares      22
Steenrod squaring operations      229
Steinberg's Lemma      153
Steinberg's theorem      307
Steinberg, R.      152 153 154
Stong — Tamagawa formula      271
Stong — Tamagawa formulae      155 255
Stong, R.E.      155 158 164
Subgroups of $\mathrm{GL}(2,\mathbb{F}_{p})$      212
Suspension      116 248
Symmetric algebra      2
Symmetric group      211
Symmetric polynomials      5
Symmetric powers      61
Symmetric product      61
System of imprimitivity      89 90
System of parameters      14 323 325
System of parameters, optimal      18
System of parameters, universal      21 139 152
Systems of parameters      99
Syzygy      13 118
Syzygy module      13
Tamagawa, T.      155
Tate complex      178
Term      3
Tetrahedral group      220
The pointwise stabilizer      289
Theorem of Hilbert — Serre      119
Toda, H.      192
Top Chern class      79
Top Dickson polynomial      155
Totalization      318
Trace formula      47 48
TRANSFER      23 33 75 151 275
Transfer homomorphism      15 29 268 310
Transfer variety      151 168
Transitivity      323
Transpotence      178
Transvection      103 156
Transvection group      158 160
Transvection groups      156
Transvector      156
Triality      192
Trigraded      316
Twisted derivation formula      189
Twisted differential      41
Two-sided Koszul complex      117
Type of a multiset      63
Underlying set      63
Unipotent subgroup      110
Unipotent subgroup of $\mathrm{GL}(n,\mathbb{F}_{q})$      110
Unique factorization domain      27
Universal system of parameters      21 139 152
Unstability condition      229
Unstability condition for modules      247
Unstable $H\odot\mathscr{P}^{*}$-module      285
Unstable $\mathbf{D}(n)\odot\mathscr{P}^{*}$-algebra      247
Unstable algebra      228
Unstable element      248
Upper bounds      16
Vandermonde determinant      35
Vanishing line      177
Vector invariants      24 147 167
Vector invariants of $\mathbb{Z}/2$      39 59
Wallflower      325
Weak relative Noether bound      205
Weyl group $W(\mathbf{F})_{4}$      192
Weyl group of type $bfF_{4}$      192
Whitney sum formula      79
Witt's theorem      276
Wreath product      89
X/G      60
Z(G)      209
Zero divisor      137
1 2 3
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